How to remove animation from duplicated object?
That's because you didn't duplicate the object (which is done by pressing Shift + D), you instanced it (done by pressing Alt + D).

The difference is that, when using the second method, all of the object's properties get linked to another's, so, editting one will result in all being modified.

To unlink a object, you use Make Single User, by pressing U, in Object Mode, which will give you a list of possible data to unlink. As you seem to only want independent animations, then choose Object Animation on the list that shows up